Figure 5.

The two parameters of spin-orbit states, β and Δℓ = ℓ_↑ − ℓ_↓ (see equation (5)), can be characterized by post-selecting on a perpendicular spin direction and obtaining: (a) the 2D intensity profile or (b) the 2D momentum distribution. The first two columns are for the state after a magnetic SPP with q = 1, the third column is for the state after a magnetic SPP with q = 2, and the last column is for the state after a magnetic SPP with q = 3. The order of rotational symmetry of the 2D intensity and momentum profiles is equal to |Δℓ| = |q| (as we set ℓ_↓ = 0 for convenience). Applying a spin rotation along ${\widehat{\sigma }}_z$ before the spin mixing effectively rotates the resulting 2D profiles. The direction of rotation determines the sign of q, and the initial azimuthal offset determines β at the detector.